Question

Consider the following supply and demand equations for rice: Qd = 100 – 8P + 0.1Y Qs = 50 + 2.4P – 2W Where Qd is quantity demanded, P is price, Y is income in thousands of dollars, Qs is quantity supplied, and W is the wage rate for labor ($/hour). Assume the following: Y = 50 W = 25 1. Compute the equilibrium price and quantity for this problem. 2. Assume that the income has increased by 10 thousand dollars. What are the equilibrium price and quantity now? 3. Compare the equilibrium price and quantity for the two equilibriums. What is the intuition behind the observed change (e.g. why did the equilibrium quantity/price increase/decrease? Why does this make sense)? Without solving mathematically, what would be the impact of a wage increase on the market outcomes? Why?

Answer 1

Question 1

Demand equation for rice is as follows -

Qd = 100 - 8P + 0.1Y

Y = 50

Qd = 100 - 8P + (0.1 * 50)

Qd = 100 - 8P + 5

Qd = 105 - 8P

Supply equation for rice is as follows -

Qs = 50 + 2.4P - 2W

W = 25

Qs = 50 + 2.4P - (2*25)

Qs = 50 + 2.4P - 50

Qs = 2.4P

At equilibrium,

Qd = Qs

105 - 8P = 2.4P

10.4P = 105

P = 105/10.4

P = 10

Q = 2.4P = 2.4 * 10 = 24

Thus,

The equilibrium price is $10 per unit.

The equilibrium quantity is 24 units.

Question 2

Now, income increases by 10 thousand dollars.

Demand equation for rice is as follows -

Qd = 100 - 8P + 0.1Y

Y = 60

Qd = 100 - 8P + (0.1 * 60)

Qd = 100 - 8P + 6

Qd = 106 - 8P

Supply equation for rice is as follows -

Qs = 50 + 2.4P - 2W

W = 25

Qs = 50 + 2.4P - (2*25)

Qs = 50 + 2.4P - 50

Qs = 2.4P

At equilibrium,

Qd = Qs

106 - 8P = 2.4P

10.4P = 106

P = 106/10.4

P = 10.19

Q = 2.4P = 2.4 * 10.19 = 24.45

Thus,

The new equilibrium price is $10.19 per unit.

The new equilibrium quantity is 24.45 units.

Question 3

The equilibrium quantity has increased from 24 units to 24.45 units.

The equilibrium price has increased from $10 per unit to $10.19 per unit.

Thus, both equilibrium price and equilibrium quantity has increased due to increase in income.

This is because when income increases, there is increase in demand.

Given the supply, increase in demand leads to increase in both equilibrium price and equilibrium quantity.

Question 4

When wage increases, cost of production increases as well.

This reduces the profit margin of firms and compel them to reduce production and thereby supply.

Given the demand, decrease in supply leads to increase in equilibrium price and decrease in equilibrium quantity.

Thus,

Wage increase would lead to increase in equilibrium price and decrease in equilibrium quantity.